Ladder Problems
A hallway that is 5 units wide and leading westward turns northward, at a corner, that leads to another hallway that is 10 units wide. If the walls are 12 units high, what is the length of the longest rod that can traverse the corner?
A 20' ladder with its foot against a building on the west side of an alley leans against a building on the east side of the alley. In a similar manner a 30' ladder with its foot against the building on the east side leans against the building on the west side. An observer at the end of the alley notices that the crossing ladders form an irregular X and that the point at which they cross is 10' above the ground. How wide is the alley?
A 15' ladder with its foot on the ground on the east side of a property fence leans against the fence and has a part of the ladder leaning over to the west side of the fence. When the sun is directly above, the part of the ladder leaning over to the west side makes a shadow on the ground of certain length. What is the largest such shadow made by the ladder over on the west side while keeping the foot of the ladder on the ground?